
where \(z^{\prime }\)  denotes a tangent vector to the boundary \(\partial D_{0}\)  at the point \(z.\)  The minus sign in front of the integral on \(\partial D_{2}\)  is here because of the orientation convention for the application of Stokes' Theorem. Following the works initiated by Burbea, see for instance [1]}, [2]}, [3]}, [4]}, we should give the equation(s) to solve by using conformal mappings. For this purpose, we shall recall Riemann mapping Theorem.
